Simplify Square Root of 69238

What is the square root of 69238 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√69238 = A√B

Unfortunately, the square root of 69238 cannot be simplified. Thus, here is the answer to the square root of 69238 in its simplest form:

√ 69238 = √ 69238

Here are two different methods we used to determine why the square root of 69238 cannot be simplified.

1) To be able to simplify the square root of 69238, one of the factors of 69238 other than 1 must be a perfect square. The factors of 69238 are 1, 2, 13, 26, 2663, 5326, 34619, and 69238. Since none of these factors are perfect squares, the square root of 69238 cannot be simplified.

2) To be able to simplify the square root of 69238, all the prime factors of 69238 cannot be unique. When we did prime factorization of 69238, we found that 2 x 13 x 2663 equals 69238. Since all the prime factors are unique, the square root of 69238 cannot be simplified.

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